Assheton Court currently features 33 flats and 13 bed sits in a two-storey building built in 1971.
The redeveloped site could have up to 70 flats across three stories, with work being completed by 2023.
At a meeting on Monday, the executive of Fareham Borough Council agreed to allocate £100,000 from the HRA Capital Development Fund to move forward with the design stage of the development.
An expanded site would help address the borough's sheltered accommodation waiting list of 170 residents, as well as helping to 'bring up standards' of the council's accommodation provision, according to council leader Sean Woodward.
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Councillor Woodward said: 'It will be a fantastic accommodation once completed.
'It is part of three schemes that will help make up the shortfall in sheltered accommodation.
The council will offer compensation for residents of the block who could be affected by the development, as well as the option to return once work is completed.
Cllr Woodward said: ‘After people have moved during a development project, we do not find that many people want to go back and will stay living somewhere else.
'That will free up more space.'
The executive approved the site to expand on to an adjacent car park, which serves the shopping precinct, on the condition that there will no net loss of parking spaces across Portchester village centre.
Councillor Roger Price said he hoped the development will see the council address the 'most unsightly part of Portchester' by improving the conditions around the Alcotts Yard.
The leader of the Liberal Democrats on Fareham Borough Council said: 'There have a lot of issues with access around the area and it would be good to give it a bit of a tidy up.
'I support what the council is doing to increase sheltered accommodation provisions - I have no problems with that.'
But Cllr Price said there was 'a desperate need' for a grocery shop in Portchester to support the area’s increasing older population
He added: 'We used to have three grocers in the precinct, and with the Co-Op leaving, many older people need somewhere else to shop that is within walking distance.'